Question: $g(x) = 2x-2$ $f(x) = -6x+4(g(x))$ $ g(f(7)) = {?} $
Solution: First, let's solve for the value of the inner function, $f(7)$ . Then we'll know what to plug into the outer function. $f(7) = (-6)(7)+4(g(7))$ To solve for the value of $f$ , we need to solve for the value of $g(7)$ $g(7) = (2)(7)-2$ $g(7) = 12$ That means $f(7) = (-6)(7)+(4)(12)$ $f(7) = 6$ Now we know that $f(7) = 6$ . Let's solve for $g(f(7))$ , which is $g(6)$ $g(6) = (2)(6)-2$ $g(6) = 10$